Chapter 4.2, Problem 76E

(a)

To determine

To explain the statement clearly.

Explanation of Solution

A randomized block design can group the subjects into blocks which have a common characteristic and thus a randomized block design allows us to take into account the change of one or more extra variables, which is in this case the excess weight of the subject.

A completely randomized design is only able to take into account the changes of the predictor variables.

(b)

To determine

To describe how to randomly assign the women to treatments using a randomized block design.

Explanation of Solution

A randomized block design can group the subjects into blocks which have a common characteristic and thus a randomized block design allows us to take into account the change of one or more extra variables.

Thus we can then best use blocks based on how overweight the subjects are, because the alphabetical order has no interesting characteristics that we want to investigate. That is, based on how overweight the subjects are.

(c)

To determine

To use technology or Table D to carry out the random assignment.

Explanation of Solution

We will form blocks of size four based on how overweight the subjects are:

  $\begin{array}{l}\text{BLOCK 1 = Birnbaum, Nevesky, Tran, Wilansky}\\ \text{BLOCK 2 = Brown, Cruz, Jackson, Stall}\\ \text{BLOCK 3 = Loren, Obrach, Rodrigues, Brunk}\\ \text{BLOCK 4 = Kendall, Marm, Santiago, Smith}\\ \text{BLOCK 5 = Deng, Moses, Williams, Hernandez}\end{array}$

Every individual in each block should receive a different treatment.

  $\begin{array}{l}\text{A=0,1}\\ \text{B=2,3}\\ \text{C=4,5}\\ \text{D=6,7}\\ \text{Ignore=8,9}\end{array}$

Line $120$ from table D:

  $35476,55972,39421,65850,04266,35436,43742,11937$

Then we obtain (the letter indicates the treatment):

  $\begin{array}{l}\text{BLOCK 1 = Birnbaum B, Nevesky C, Tran D, Wilansky A}\\ \text{BLOCK 2 = Brown D, Cruz C, Jackson B, Stall A}\\ \text{BLOCK 3 = Loren B, Obrach C, Rodrigues B, Brunk A}\\ \text{BLOCK 4 = Kendall A, Marm D, Santiago C, Smith B}\\ \text{BLOCK 5 = Deng C, Moses A, Williams B, Hernandez D}\end{array}$